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leeye84

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Two watermelons of the same sort, A and B, are on sale. Watermelon A has circumference of 60 cm, watermelon B, of 50 cm. If Watermelon A is 1.5 times more expensive than Watermelon B, which watermelon is a better buy? (assume watermelon is spherical in shape)

A) A
B) B
C) Either
D) Neither
E) Impossible

Please explain.

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leeye84

A is better

PriceA / Price B = 1.5
If you find the ratio of volume to be greater, then it is a better buy.
Volume of Sphere = (4/3) * P * R^3
Va / Vb = (Ra / Rb)^3

Ra = 60 / (2*P) = 30 / P
Rb = 50 / (2*P) = 25 / P

Va / Vb = (30/25)^3 = (1.2)^3 = 1.728
A is a better buy.

Whatever

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My answer is A - the same method as bkk145, but this is exactly the question where I think too much - what about density, weight, taste? We cannot make a decision based only on volume =)

leeye84

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leeye84

fantastic explaination. I wish every answer is posted with as much detail as your answer.

StartupAddict

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Pretty easy question

calculate volumes

have to know

circumference = 2*pi*diameter

diamter = 2*radius

volume of sphere = 4/3 * pi * radius^3

then assume A costs 1.5, and B costs 1

then see how many cubic centimeters you get per dollar........... with A you get 304, with B you get ~264

A is the better buy

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Two watermelons, $A$ and $B$ , are on sale. Watermelon $A$ has a circumference of 6 inches; watermelon $B$ , 5 inches. If the price of watermelon $A$ is 1.5 times the price of watermelon $B$ , which watermelon is a better buy?

(Assume that the two watermelons are spheres).

(A) A
(B) B
(C) Neither
(D) Both
(E) Impossible to determine

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Source: GMAT Club Tests - hardest GMAT questions

Answer:To determine a better buy - we need to find out which watermelon is cheaper per kilo. Watermelon with C=60 has a volume of 224,694,718 (cu. cm's?) and the watermelon with C=50 has volume of 130,031,759. C=60 watermelon is 1.7 times the size of C=50 watermelon. Therefore C=60 is obviously the better buy.

My questions: How do we come up with these two volumes with the equation 4/3 pie r^3. Also, what circumference equation is used to determine r in the sphere? I thought the circumference can only be determined on a 2 dimensional object and not a 3 dimensional one (sphere). Thank you.

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maratikus

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24 Sep 2008, 18:26

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dczuchta

Two watermelons of the same sort, A and B, are on sale. Watermelon A has circumference of 60 cm, watermelon B, of 50 cm. If the price of watermelon A is 1.5 times the price of watermelon B, which watermelon is a better buy?

(You may assume that the watermelon is spherical in shape)

Answer:To determine a better buy - we need to find out which watermelon is cheaper per kilo. Watermelon with C=60 has a volume of 224,694,718 (cu. cm's?) and the watermelon with C=50 has volume of 130,031,759. C=60 watermelon is 1.7 times the size of C=50 watermelon. Therefore C=60 is obviously the better buy.

My questions: How do we come up with these two volumes with the equation 4/3 pie r^3. Also, what circumference equation is used to determine r in the sphere? I thought the circumference can only be determined on a 2 dimensional object and not a 3 dimensional one (sphere). Thank you.

here is what's important.

Radius of A = R_a
Radius of B = R_b

R_a/R_b = circumference of A/circumference of B = 6/5
Therefore the ratio of volumes of A and B is 6^3/5^3

Price of A/Price of B should be 6^3/5^3 if they are priced fairly
Since actual Price of A/Price of B = 1.5 < 1.7 < 6^3/5^3 -> A is a better buy
I hope that helps.

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1. Two watermelons of the same sort, A and B, are on sale.
Watermelon A has circumference of 60 cm, watermelon B, of 50 cm.
If the price of watermelon A is 1.5 times the price of watermelon B, which watermelon is a
better buy?

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To get the better buy, we need to make sure we get more volume for the price.

Watermelon A
2*pi*R1 = 60 ==> R1 = 30/pi
Volume of A = (4/3) pi (R1^3) = (4/3)*pi*((30/pi)^3) = (4/3) * 3.14 * (30/3.14)^3 = 4 * 10^3 = appr 4000

Watermelon B
2*pi*R2 = 50 ==> R2 = 25/pi
Volume of B = (4/3) pi (R2^3) = (4/3)*pi*((25/pi)^3) = 4/3 * 3.14 * (25/3.14)^3 = 4 * 8^3 = appr 2000

So if v get watermelon B for 10 dollars, we'll need to pay $20 to get 2 watermelons which will be 4000units which is equal to watermelon A.

so its always better to pay $15 to get watermelon A, since we r getting 4000units for $15.

S.

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sumanamba

Good One. The key is to identify that circle is 2-D & sphere is circle's 3-D form.

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how do we know that the watermelons are perfect spheres?

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bigtreezl

how do we know that the watermelons are perfect spheres?

Just because we have no other information regarding shape here and we are given only the circumferences, we are forced to assume it is a sphere

I am not sure if this is a GMAT type question. GMAC prefers to leave no ambiguities in their questions.

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26 Sep 2008, 20:23

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This is the solution i got from the gmat club test.
To determine a better buy - we need to find out which watermelon is cheaper per kilo. Watermelon with C=60 has a volume of 224,694,718 (cu. cm's?) and the watermelon with C=50 has volume of 130,031,759. C=60 watermelon is 1.7 times the size of C=50 watermelon. Therefore C=60 is obviously the better buy.

I was just wondering how they came up with the volume?

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study

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30 Oct 2008, 06:15

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It's B.

I look at it as a dimension/price ratio: 60:1,5 for watermelon A, 50:1 watermelon B. Thus, watermelon B worths more than A.

Right?

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I think A is the best buy as the volume of the watermelon is important.
The volume is 4/3pi*r^3
so the radius of watermelon A= 30/pi
watermelon B=25/pi
So keeping the 4/3 and pi constant the ratio of volume is 30*30*30/25*25*25=1.7
But the price of A is 1.5 times of B where as the volume of A is 1.7 times of B.
So I think A is the best buy

What is the OA??

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subarao

Definitely we need to consider weight not area or redius/diameter or circumference.

subarao

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30 Oct 2008, 11:09

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Will it be considered that the watermelon with greater volume will be of greater weight? (well, then we have to assume the densities of the both watermelon are same).
If not then, the condition is not sufficient enough.

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so it is impossible to determine from the above information. Am I right GMAT tiger?

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A's volume is about 1.7 times bigger than B's, therefore A is a better buy. But... every time I come up with smth like that the answer is E, because... watermellon A can be rotten inside and from info above it is impossible to determine.